Finite Group DatabasebetaFinite Group Databasebeta| order | 576 |
| isoclinism | isoclinic class of #63419 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | C42⋊C9 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #63419 |
| commutator, hypocenter | C42⋊C9 | C4 |
| Frattini, socle, prime radical | C23×C3 | S4 |
| Fitting | C2×C3×C42 | D3 |
| cosocle | C2×C42⋊C9 | C2 |
| LCS | G ▷ C42⋊C9 | |
| UCS | C1 ◁ C2 | |
87 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^2,3^2,2^4|a^2=b,c^3=d^2,e^2=gh,f^2=g,c^a=c^2d,d^a=d^2,e^a=f,f^a=e,g^a=gh,e^c=f,f^c=efh,g^c=h,h^c=gh36 conjugacy classes — view the full character table.
| maximal subgroup of | #11919935, C4×#63419, #11919947, … |
| maximal normal subgroup of | #11919935, C4×#63419, #11919947, … |
| maximal quotient of | #11919923, #11919924, #11919925, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(576, 185);